Preprint/Report

PUBDB-2016-06688

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Cyclic tridiagonal pairs, higher order Onsager algebras and orthogonal polynomials

Baseilhac, P. (Corresponding author) ; Gainutdinov, A. (Corresponding author)DESY* ; Vu, T. T. (Corresponding author)

2016

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Please use a persistent id in citations: doi:10.3204/PUBDB-2016-06688

Report No.: ZMP-HH-16-10; Hamburger Beitr ̈age zur Mathematik 595; arXiv:1607.00606

Abstract: The concept of cyclic tridiagonal pairs is introduced, and explicit examples are given. For a fairly general class of cyclic tridiagonal pairs with cyclicity N, we associate a pair of `divided polynomials'. The properties of this pair generalize the ones of tridiagonal pairs of Racah type. The algebra generated by the pair of divided polynomials is identified as a higher-order generalization of the Onsager algebra. It can be viewed as a subalgebra of the q-Onsager algebra for a proper specialization at q the primitive 2Nth root of unity. Orthogonal polynomials beyond the Leonard duality are revisited in light of this framework. In particular, certain second-order Dunkl shift operators provide a realization of the divided polynomials at N=2 or q=i.

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Contributing Institute(s):

1. Theorie-Gruppe (T)

Research Program(s):

1. 611 - Fundamental Particles and Forces (POF3-611) (POF3-611)

Experiment(s):

1. No specific instrument

Appears in the scientific report 2016

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Database coverage:
; ; Published

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Linked articles:

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Journal Article Baseilhac, P. (Corresponding author) ; Gainutdinov, A.DESY* ; Vu, T. T.
Cyclic tridiagonal pairs, higher order Onsager algebras and orthogonal polynomials
Linear algebra and its applications 522, 71 - 110 (2017) [10.1016/j.laa.2017.02.009]2017     Files  Fulltext by arXiv.org BibTeX | EndNote: XML, Text | RIS

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